On S-cluster sets and S-closed spaces

Abstract

A new type of cluster sets, called S-cluster sets, of functions and multifunctions between topological spaces is introduced, thereby providing a new technique for studying S-closed spaces. The deliberation includes an explicit expression of S-cluster set of a function. As an application, characterizations of Hausdorff and S-closed topological spaces are achieved via such cluster sets.

Keywords

• S-cluster set
• S-closedness
• θs-closure
• semi-open sets.